Lagrangian systems subject to fractional damping can be incorporated into a variational formalism. The construction can be made by doubling the state variables and introducing fractional derivatives \cite{JiOb2}. The main objective of this paper is to use the Runge-Kutta convolution quadrature (RKCQ) method for approximating fractional derivatives, combined with higher order Galerkin methods in order to derive fractional variational integrators (FVIs). We are specially interested in the CQ based on Lobatto IIIC. Preservation properties such as energy decay as well as convergence properties are investigated numerically and proved for 2nd order schemes. The presented schemes reach 2nd, 4th and 6th accuracy order. A brief discussion on the midpoint fractional integrator is also included.

翻译：受分数阶阻尼作用的拉格朗日系统可纳入变分框架。该构造可通过将状态变量加倍并引入分数阶导数实现 \cite{JiOb2}。本文的主要目标是采用Runge-Kutta卷积求积（RKCQ）方法逼近分数阶导数，并结合高阶伽辽金方法推导分数阶变分积分器（FVIs）。我们特别关注基于Lobatto IIIC的卷积求积方法。通过数值实验研究了能量衰减等守恒性质与收敛特性，并对二阶格式给出了理论证明。所提出的格式可达到二阶、四阶和六阶精度。文中亦包含对中点分数阶积分器的简要讨论。